source file: mills2.txt Date: Thu, 19 Jun 1997 05:41:46 +0200 Subject: Mea Culpa (Dorian/Phrygian Mode) From: John Chalmers Paul E is correct. I added 22 as an afterthought just as I was posting and it was a mistake, though my observation that a recognizable Pythagorean-type Greek Phrygian/Ecclesiastical Dorian exists in 22 and 17 is correct. It is difficult to come up with a satisfactory tuning for the Greek Phrygian/Eccl. Dorian mode in 22. The best I have found is either the all-pythagorean 4 1 4 4 4 1 4 (as Paul mentioned) or the mixed 4 2 3 4 4 2 3 which has an inharmonic pythagorean triad on its subdominant and the usual 22-tet minor triads on the tonic and dominant. The trichordal variety with a major triad on the subdominant has an equally-divided upper tetrachord: 4 2 3 4 3 3 3. The major (Lydian) mode itself is 4 3 2 4 3 4 2. Twenty-two, at least has a well-defined Pythagorean diatonic 4 4 1 4 4 4 1. Similar problems arise in 15 tet as well where the "nearly just" major mode is 3 2 1 3 2 3 1 and the P/D mode is 3 1 2 3 2 2 2 or 3 1 2 3 3 1 2 with the chord on the subdominant as 6 3 rather than 4 5 or 4 5. One might also try 3 1 2 3 2 1 3, but then the chord on the dominant will be 3 6 (0 3 9 on degree 9). --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 19 Jun 1997 15:33 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05271; Thu, 19 Jun 1997 15:33:47 +0200 Date: Thu, 19 Jun 1997 15:33:47 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05317 Received: (qmail 6720 invoked from network); 19 Jun 1997 13:33:20 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 19 Jun 1997 13:33:20 -0000 Message-Id: <009B604E698D0F09.07AF@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu